Abstract
Symmetrized wave functions of 4- and 5-atom molecules with two, three, or four identical atoms are constructed in general form. The symmetrization of the angular and radial parts of the vibrational-rotational wave function is examined in detail. The representation matrix and the Clebsch-Gordan coefficients of the permutation group Sn (n = 3, 4) are adapted for the use in molecular spectroscopy. This makes it easier to draw analogies with the theory of effective Hamiltonian. The use of symmetrized wave functions is shown to significantly alleviate the problem of calculating the vibrational-rotational energy levels from the potential energy surface for such molecules as CH4, CH3D, CH3Cl, etc.
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